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Evaluate:

\(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\)

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\(\lim\limits_{x \to 5}\frac{e^x-e^5}{x-5}\) 

\(=\lim\limits_{x \to 0}\frac{e^{n+5}-e^5}{n}\)  [Let x – 5 = n ⇒ as x - 5, n → 0]

\(=\lim\limits_{x \to 0}\frac{e^5(e^n-1)}{n}\) 

\(=e^5\lim\limits_{x \to 0}\frac{e^n-1}{n}\) 

\(=e^5.1 \) 

\(=e^5\)

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